binomial_options_pricing_posts.txt

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BINOMIAL OPTIONS PRICING - SOCIAL MEDIA POSTS
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1. TWITTER/X (< 280 characters)
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How do you price an option before it expires?

The binomial model breaks time into steps where prices go UP or DOWN. Work backwards from payoff to find fair value.

American put premium: 0.11 over European!

#QuantFinance #Python #Options

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2. BLUESKY (< 300 characters)
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Implemented the Cox-Ross-Rubinstein binomial options pricing model in Python.

Key insight: price can only move up (u = e⁽σ√Δt)) or down (d = 1/u) at each step.

With 300 steps, European options converge to Black-Scholes within 0.001.

American puts show early exercise premium of ~0.11.

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3. THREADS (< 500 characters)
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Ever wonder how traders price options before they expire?

The binomial model is beautifully simple: at each time step, the stock price either goes UP or DOWN by a fixed factor.

Starting from the final payoff (max(S-K, 0) for calls), you work backwards using risk-neutral probabilities to find today's fair price.

The magic: as you add more steps, it converges to the famous Black-Scholes formula!

Built this in Python with numpy - American puts show a 0.11 early exercise premium over European puts.

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4. MASTODON (< 500 characters)
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New notebook: Binomial Options Pricing Model

Implemented the CRR parameterization where:
• u = e⁽σ√Δt), d = 1/u
• Risk-neutral probability: p = (e⁽rΔt) - d)/(u - d)

Key findings with S₀=K=100, σ=20%, r=5%, T=1yr:
• European call: 10.4506 (vs BS: 10.4506)
• American put premium: 0.1104 over European
• Convergence rate: O(1/N)

American calls = European calls (no dividend case).

#QuantFinance #Python #ComputationalFinance

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5. REDDIT (r/learnpython or r/QuantFinance)
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Title: Built a Binomial Options Pricing Model in Python - Here's What I Learned

Body:

**What is it?**

The Binomial Options Pricing Model is a way to calculate what an option should cost today. Think of it like this: imagine a stock price that can only go UP or DOWN at each time step (like a coin flip, but weighted). Starting from the final payoff at expiration, you work backwards to find today's fair price.

**The Math (simplified)**

At each step Δt:
- Price goes up by factor u = e⁽σ√Δt)
- Price goes down by factor d = 1/u
- Risk-neutral probability: p = (e⁽rΔt) - d)/(u - d)

Then discount back: V = e⁽-rΔt) × [p × V_up + (1-p) × V_down]

**What I Implemented**

- Full binomial tree with backward induction
- Both European and American options (calls and puts)
- Black-Scholes comparison for validation

**Key Results**

With S₀ = 100, K = 100, T = 1 year, r = 5%, σ = 20%:

| Option Type | Binomial (N=300) | Black-Scholes |
|------------|-----------------|---------------|
| European Call | 10.4506 | 10.4506 |
| European Put | 5.5735 | 5.5735 |
| American Put | 5.6839 | N/A |

**Interesting Findings**

1. American calls = European calls (for non-dividend stocks) because it's never optimal to exercise early
2. American puts have an early exercise premium (~0.11) because you might want to exercise early if the stock crashes
3. Convergence is ~O(1/N), so 300 steps gets you within 0.001 of Black-Scholes

**View the Full Notebook**

You can run and modify this code directly in your browser:
https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/binomialₒptions_pricing.ipynb

The visualization shows convergence plots and the early exercise premium for American puts.

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6. FACEBOOK (< 500 characters)
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How do financial markets price options?

The Binomial Model breaks it down elegantly: at each moment, a stock can only go UP or DOWN. By working backwards from the expiration payoff, we find today's fair price.

Cool finding: American put options are worth MORE than European puts (5.68 vs 5.57) because you can exercise early if the stock crashes!

Built this model in Python - watch it converge to the famous Black-Scholes formula.

Explore the interactive notebook: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/binomialₒptions_pricing.ipynb

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7. LINKEDIN (< 1000 characters)
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Implementing the Binomial Options Pricing Model: A Computational Finance Exercise

I recently built a Python implementation of the Cox-Ross-Rubinstein (1979) binomial options pricing model, demonstrating fundamental concepts in derivatives valuation.

Technical Implementation:
• Vectorized NumPy computation for efficient backward induction
• Risk-neutral pricing framework: p = (e⁽rΔt) - d)/(u - d)
• Support for both European and American-style options

Key Validation Results (S₀=K=100, σ=20%, r=5%, T=1yr):
• European options converge to Black-Scholes within 0.001 at N=300 steps
• American put early exercise premium: 0.11 (reflecting optimal stopping)
• Convergence rate approximately O(1/N)

The model illustrates core principles: no-arbitrage pricing, risk-neutral valuation, and the relationship between discrete and continuous-time models.

Skills demonstrated: Python, NumPy, SciPy, financial mathematics, Monte Carlo alternatives, computational efficiency.

View the complete analysis and code:
https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/binomialₒptions_pricing.ipynb

#QuantitativeFinance #Python #DerivativesPricing #ComputationalFinance #FinancialEngineering

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8. INSTAGRAM (< 500 characters)
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Options Pricing Demystified

The binomial model shows how options get their value:

At each time step, stock prices can only go UP or DOWN

Work backwards from the final payoff to find today's price

As steps → ∞, it becomes the famous Black-Scholes formula

Built this in Python with full convergence analysis

American puts are worth MORE than European puts because early exercise has value when stocks crash

Swipe to see the convergence plots!

#QuantFinance #Python #DataScience #Finance #Coding #Mathematics #Trading #Options #Algorithms

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